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Simplifying -4.9t2 + 355t + 87 = 0 Reorder the terms: 87 + 355t + -4.9t2 = 0 Solving 87 + 355t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -17.75510204 + -72.44897959t + t2 = 0 Move the constant term to the right: Add '17.75510204' to each side of the equation. -17.75510204 + -72.44897959t + 17.75510204 + t2 = 0 + 17.75510204 Reorder the terms: -17.75510204 + 17.75510204 + -72.44897959t + t2 = 0 + 17.75510204 Combine like terms: -17.75510204 + 17.75510204 = 0.00000000 0.00000000 + -72.44897959t + t2 = 0 + 17.75510204 -72.44897959t + t2 = 0 + 17.75510204 Combine like terms: 0 + 17.75510204 = 17.75510204 -72.44897959t + t2 = 17.75510204 The t term is -72.44897959t. Take half its coefficient (-36.2244898). Square it (1312.213661) and add it to both sides. Add '1312.213661' to each side of the equation. -72.44897959t + 1312.213661 + t2 = 17.75510204 + 1312.213661 Reorder the terms: 1312.213661 + -72.44897959t + t2 = 17.75510204 + 1312.213661 Combine like terms: 17.75510204 + 1312.213661 = 1329.96876304 1312.213661 + -72.44897959t + t2 = 1329.96876304 Factor a perfect square on the left side: (t + -36.2244898)(t + -36.2244898) = 1329.96876304 Calculate the square root of the right side: 36.46873679 Break this problem into two subproblems by setting (t + -36.2244898) equal to 36.46873679 and -36.46873679.Subproblem 1
t + -36.2244898 = 36.46873679 Simplifying t + -36.2244898 = 36.46873679 Reorder the terms: -36.2244898 + t = 36.46873679 Solving -36.2244898 + t = 36.46873679 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '36.2244898' to each side of the equation. -36.2244898 + 36.2244898 + t = 36.46873679 + 36.2244898 Combine like terms: -36.2244898 + 36.2244898 = 0.0000000 0.0000000 + t = 36.46873679 + 36.2244898 t = 36.46873679 + 36.2244898 Combine like terms: 36.46873679 + 36.2244898 = 72.69322659 t = 72.69322659 Simplifying t = 72.69322659Subproblem 2
t + -36.2244898 = -36.46873679 Simplifying t + -36.2244898 = -36.46873679 Reorder the terms: -36.2244898 + t = -36.46873679 Solving -36.2244898 + t = -36.46873679 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '36.2244898' to each side of the equation. -36.2244898 + 36.2244898 + t = -36.46873679 + 36.2244898 Combine like terms: -36.2244898 + 36.2244898 = 0.0000000 0.0000000 + t = -36.46873679 + 36.2244898 t = -36.46873679 + 36.2244898 Combine like terms: -36.46873679 + 36.2244898 = -0.24424699 t = -0.24424699 Simplifying t = -0.24424699Solution
The solution to the problem is based on the solutions from the subproblems. t = {72.69322659, -0.24424699}
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